Question

A where and a cylinder have the same radius and height . The volume of the cylinder is 48 cm 3. What is the volume of the sphere?

Answer 1

Given:

Sphere and cylinder have same radius and height.

Volume of the cylinder = 48 cm³

To find:

The volume of the sphere.

Solution:

Radius and height of cylinder are equal.

⇒ r = h

Volume of cylinder:

$V=\pi r^2h$

Substitute the given values.

$48=\pi r^2r$   (since r = h)

$48=\pi r^3$

$48=3.14 \times r^3$

Divide by 3.14 on both sides.

$\frac{48}{3.14} =\frac{3.14\times r^3}{3.14}$

$15.28=r^3$

Taking cube root on both sides, we get

2.48 = r

The radius of the cylinder is 2.48 cm.

Sphere and cylinder have same radius and height.

Volume of sphere:

$V=\frac{4}{3} \pi r^3$

$V=\frac{4}{3} \times 3.14 \times (2.48)^3$

$V=63.85$

The volume of the sphere is 63.85 cm³.